n-strongly Gorenstein Projective and Injective and Flat Modules

In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applications are given.

Notes on Strongly n-Gorenstein Projective, Injective and Flat Modules

In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.

A Generalization of Gorenstein Injective and Flat Modules

In this article, we introduce and study the concept of n-Gorenstein injective （resp., n-Gorenstein flat） modules as a nontrivial generalization of Gorenstein injective （resp., Gorenstein flat） modules. We investigate the properties of these modules in various ways. For example, we show that the class of n-Gorenstein injective （resp., n -Gorenstein flat） modules is closed under direct sums and direct products for n ≥ 2. To this end, we first introduce and study the notions of n-injective modules and n-flat modules.

Y-Gorenstein Cotorsion Modules

Let R be an associative ring with identity,and Y be a class of right R-modules,which contains all injective right R-modules.In this paper,we introduce the definition of Y-Gorenstein cotorsion modules,which is a generalization of cotorsion and Gorenstein cotorsion modules.We discuss the relationship between Gorenstein cotorsion,weakly Gorenstein cotorsion and Y-Gorenstein cotorsion modules.We investigate properties and characterizations of Y-Gorenstein cotorsion modules.

PS-injective Modules, PS-flat Modules and PS-coherent Rings

A left ideal I of a ring R is small in case for every proper left ideal K of R, K ＋ I ≠R. A ring R is called left PS-coherent if every principally small left ideal Ra is finitely presented. We develop, in this paper, PS-coherent rings as a generalization of P-coherent rings and J-coherent rings. To characterize PS-coherent rings, we first introduce PS-injective and PS-flat modules, and discuss the relation between them over some spacial rings. Some properties of left PS-coherent rings are also studied.

ABSOLUTELY E-PURE MODULES AND E-PURE SPLIT MODULES

We first introduce the concepts of absolutely E-pure modules and E-pure split modules. Then, we characterize the IF rings in terms of absolutely E-pure modules. The E-pure split modules are also characterized.

Flatly Broadened and Highly Coherent Supercontinuum Generation by Induced Modulation Instability in ANDi-PCF

In this paper, a flatly broadened and highly coherent supercontinuum generation by induced modulation instability in ANDi-PCF is proposed. The numerical results show that the bandwidth of supercontinuun can be increased by increasing the modulation depth and the coherence property of supercontinuum can be improved with the optimal modulation frequency. A highly coherent supercontinuum with the 10 dB bandwidth of 1305 nm and the flatness of less than 10 dB can be obtained when seeding at the modulation depth of 0.3 and modulation frequency of 24 THz.

Y-Gorenstein模类导出的对偶对

在X-Gorenstein投射模、Y-Gorenstein内射模以及Y-Gorenstein平坦模的基础上,进一步研究由Y-Gorenstein模类导出的对偶对(~⊥YGI,YGF~⊥)及(YGI,YGF).

Y-Gorenstein余挠维数

设R是有单位元的结合环,Y是一个包含所有内射模的右R-模类.给出Y-Gorenstein余挠模的概念,它是余挠模和Gorenstein余挠模的一个推广.研究左R-模M的Y-Gorenstein余挠维数小于等于n的若干等价刻画,并讨论了左R-模短正合列0→U→V→W→0中各项的Y-Gorenstein余挠维数之间的关系.

Amplitude modulation and extreme events in turbulent channel flow

Amplitude modulation of near-wall turbulence by large-scale structures in the outer layer is investigated by direct numerical simulation of turbulent channel flows at Reynolds number Re= 540, 1000, 2000. The effect of modulation is obvious in the two-point cross-section correlation map, and the correlation coefficients increase significantly with the Reynolds number. The influence of modulation is reflected in the tail of the probability density function of the near-wall flow signals, which expands as the Reynolds number increases. The flatness factor provides a quantitative description of the high fluctuation events due to modulation. Vortical structures associated with modulation are revealed by conditionally averaging the flow field of the near-wall extreme events, providing a depiction of how the influence of the large-scale structures penetrate towards the near-wall region.

Magnetic-fluid microelectromechanical light modulator

A new microfluidic microelectromechanical light modulator using a magnetic fluid is introduced. The optical reflection from the device is modulated by applying an electric current into an electrode, which is enclosed by ferromagnetic thin films as in an inductive head for a magnetic data storage device. The magnetic field produced by the current exerts a magnetic force on the magnetic fluid and drives the fluid to cover the cell surface. The surface tension of the fluid provides a restoring force when the field is reduced. The actuation of the fluid is completed in about 12 ms for both thin-to-thick and thick-to-thin fluid film switchings by magnetic forces and surface tension forces, respectively. It was observed that the switching speed was almost independent of the driving current, and no considerable thermal effect were observed when driven by a current up to 100 mA.

High Performance Asymmetric Three Corrugation-Pitch-Modulated DFB Lasers Suitable for Stable Single Longitudinal Mode Operation

This paper presents an optimized asymmetric three corrugation-pitch-modulated DFB laser (3CPM-DFB) with extremely high mode selectivity(△αL= 0.97) and low flatness(F = 0.009), which are two key parameters to indicate the laser’s single longitudinal mode(SLM) performance. In threshold analysis, the optimization process based on transfer matrix method is demonstrated to maximize △αL?and minimize F simultaneously. In the above-threshold regime, the evolutions of △αL?and?longitudinal distribution of photon density with injection current are evaluated. More importantly, nanoimprint lithography which was proved an efficient way to fabricate DFB gratings can provide completely same simple fabrication procedure for both 3CPM grating and conventional uniform grating. So the big practical value of 3CPM-DFB can be expected because of its advanced performance and easy manufacturability.

IFP-FLAT DIMENSIONS AND IFP-INJECTIVE DIMENSIONS

In basic homological algebra, the flat and injective dimensions of modules play an important and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions are introduced and studied. We show that IFP-fd（M） = IFP-id（M＋） and IFP-fd（M＋）=IFP-id（M） for any R-module M over any ring R. Let ：Z-In （resp., ＂Zgv,~） he the class of all left （resp., right） R-modules of IFP-injective （resp., IFP-flat） dimension at most n. We prove that every right R-module has an IFn- preenvelope, （IFn,IF⊥n） is a perfect cotorsion theory over any ring R, and for any ring R with IFP-id（RR） 〈 n, （IIn,II⊥n） is a perfect cotorsion theory. This generalizes and improves the earlier work （J. Algebra 242 （2001）, 447-459）. Finally, some applications are given.

On the Flatness and Injectivity of Dual Modules(II)

For a commtative ring R and an injective cogenerator E in the category of R-modules, we characterize QF rings, IF rings and semihereditary rings by using the properties of the dual modules with respect to E.

Strongly Gorenstein Flat Modules and Dimensions

There is a variety of nice results about strongly Gorenstein flat modules over coherent rings. These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of these results, and to give homological descriptions of the strongly Gorenstein flat dimension (of modules and rings) over arbitrary associative rings.

Remarks on Gorenstein Weak Injective and Weak Flat Modules

In this paper,we introduce Gorenstein weak injective and weak flat modules in terms of,respectively,weak injective and weak flat modules;the classes of Gorenstein weak injective and weak flat modules are larger than the classical classes of Gorenstein injective and flat modules.In this new setting,we characterize rings over which all modules are Gorenstein weak injective.Moreover,we discuss the relation between the weak cosyzygy and Gorenstein weak cosyzygy of a module,and also the stability of Gorenstein weak injective modules.

多相移间插取样光纤光栅滤波器的设计与优化

【目的】取样光纤布拉格光栅(SFBG)以其梳状滤波特性引起人们的普遍关注,成为光纤光栅技术研究的新热点。显然,设计具有高通道数、平顶和窄带宽的光学滤波器具有重要的工程意义。文章提出了一种插入多相移(MPS)的间插取样光纤布拉格光栅(ISFBG)滤波器。【方法】ISFBG具有大量反射通道,通过插入MPS,可引入多个平顶窄传输通道。通过优化插入ISFBG的两个π相移的位置,首先设计了具有41个传输通道的光学滤波器,该滤波器覆盖C波段,通道间隔为100 GHz,每个传输通道都具有平顶响应,3 dB带宽较窄(<1 GHz),形状因子较小(<3.2)。接着,保持其他结构不变,通过优化插入3个π相移的位置,可在此基础上进一步减小形状因子,从而改善传输通道的矩形形状。通过引入MPS技术,设计了插入3个π相移的ISFBG,可实现通道数目加倍,通道间隔减半。【结果】演示了一种通道数目为81的平顶窄带宽的光学滤波器,该滤波器覆盖C波段,通道间隔为50 GHz,多通道的3 dB带宽为900.5 MHz,形状因子接近2.17。同时讨论了MPS的大小、位置和光纤的等效长度的精度对于实际制造的影响。【结论】所设计的滤波器具有较高通道数,每个通道都具有平顶响应且带宽较窄,符合设计目的。这种滤波器在多波长激光器和多波段微波信号处理系统中具有潜在的应用前景。

Morita环上的F-Gorenstein平坦模

设Λ(0,0)=(^(A)^(M)^(N)_(B))是Morita环,其中A和B是环,N为(A,B)-双模,M为(B,A)-双模.证明了若双模M和N满足某些条件,则函子T A:Mod-A→Mod-Λ(0,0)和T B:Mod-B→Mod-Λ(0,0)保持F-Gorenstein平坦性.

Frobenius扩张下的PGF■n-模与Gorenstein■n-平坦模

设R■S是环的Frobenius扩张,M是一个S-模.证明如果R■S是可分Frobenius扩张,则SM是投射余可解的Gorenstein■n-平坦模(Gorenstein■n-平坦模)当且仅当RM是投射余可解的Gorenstein■n-平坦模(Gorenstein■n-平坦模).

Gorenstein(L,A)-投射模的稳定性

设R是有单位元的交换环,(L,A)是完备的对偶对.先引入一种相对于完备对偶对(L,A)的Gore nstein同调模类GP(2)L,再研究GP(2)/L的一些性质.最后,借助一些特殊的模类证明GP(2)L与Gorenstein(L,A)-投射模类一致.